Structure of the Radial Electric Field and Toroidal/Poloidal Flow in High Temperature Toroidal Plasma

Transcription

1 J. Plasma Fusion Res. SERIES, YoL.4 (20O1) 3G42 Structure of the Radial Electric Field and Toroidal/Poloidal Flow in High Temperature Toroidal Plasma IDA Katsumi*, CHS Group, LHD Group and JFT2M Group' National Institute for Fusion Science, Toki , Japan 1) Japa, Atomic Energy Research Institute, Nakamachi, Nakagun, Ibaragi,319ll, Japan (Received: 5 December 2000 / Accepted: 18 August 2001) Abstract The structure of the radial electric field and toroidal/poloidal flow is discussed for the high temperature plasma in torodidal syste, tokamak and Heliotron type magnetic configurations. The spontaneous toroidal and poloidal flows are observed in the plasma with improved confinement. The radial electric field is mainly determined by the poloidal flow, because the contribution of toroidal flow to the radial electric field is small. The jump of radial electric field and poloidal flow are commonly observed near the plasma edge in the socalled high confinement mode (Hmode) plasmas in tokamaks and electron root plasma in stellarators including Heliotrons. In general the toroidal flow is driven by the momentum input from neutral beam injected toroidally. There is toroidal flow not driven by neutral beam in the plasma and it will be more significant in the plasma with large electric field. The direction of these spontaneous toroidal flows depends on the symmetry of magnetic field. The spontaneous toroidal flow driven by the ion temperature gradient is in the direction to increase the negative radial electric field in tokamak. The direction of spontaneous toroidal flow in Heliotron plasmas is opposite to that in tokamak plasmas because of the helicity of symmetry of the magnetic field configuration. Keywords: radial electric field, toroidal plasma 1. lntroduction A radial electric field has been considered to possibly reduce the ripple loss and to prevent the degradation of confinement in stellarators and helical devices [1]. This is because the neoclassical transport t2,31 is expected to become more important at higher temperature and low collisionality plasmas [a]. In tokamaks. after the transition from low confinement mode (Lmode) to high confinement mode (Hmode [5]) (L/H transition) was found in ASDEX, a spontaneous bifurcation of the radial electric field was theoretically proposed to cause it and thus refreshed the motivation of research t6,?1. The phenomenon, that, associated with the L/H transition, the radial electric field suddenly * C o rre s ponding author' s e mail : nifs. ac.j p changes at the plasma periphery (few cm), was observed in DIIID [8], JFT2M t9,l0l, ASDEX [11]' The importance of the radial electric field for the Hmode is now widely recognized. There are two important mechanis in the formation of the radial electric field, one is the damping term, which is viscosity in plasma rotations, and the other is a driving force to rotate the plasmas toroidally or poloidally. In the damping term, both the neoclassical parallel viscosity and perpendicular viscosity are discussed. There are external and internal driving forces; the external forces are momentum input or jxb and the internal forces are ion and electron nonambipolar flux by The Japan Society of Plasma Science and Nuclear Fusion Research 36

2 IdaK. et al., Structure of the Radial Electric Field and Toroidal/Poloidal Flow in High Temperature Toroidal plasma (ion and electron loss induced radial current) due to density and/or temperature gradient or orbit loss. 2. Spontaneous Poloidal Flow A spontaneous poloidal flow has been recognized to be important in the confinement of toroidal plasmas, since poloidal flow velocity and radial electric field shear were found to contribute an improvement of plasma confinement in Hmode plasmas t8101. The turbulence in the plasma is predicted to be suppressed by a E x B velocity shear through the mechanism of a nonlinear decorrelation [12,131. It has been confirmed experimentally that the E x B shearing rate exceeds the growth rate of the turbulence at the transport barrier u4,lsl. 2.1 Spontaneous Poloidal Flow in Tokamaks The poloidal flow is in the electron diamagnetic direction and appears suddenly near the plasma edge at the Hmode transition. The poloidal rotation velocity profile in Hmode has a peak at the separatrix. No critical normalized ion collisionality, v*;, for the transition of L to Hmode is observed. The size of the poloidal flow in Hmode has no dependence on potoidal gyroradius. The poloidal rotation velocity profiles and ion temperature profiles at ohmic, Lmode and Hmode phase are shown in Figure 1(a). The plasma always rotates in the ion diamagnetic direction outside the separatrix and in the electron diamagnetic direction inside the separatrix. The position, where the plasma does not rotate poloidally, moves outward as the plasma changes from ohmic to L to Hmode. The poloidal flows outside and inside the separatrix are in the opposite direction to each other. 2.2 Spontaneous Poloidal Flow in Helical System In the Large Helical Device (LHD) the transition from negative electric field (ion root) to positive electric field (electron root) is observed for the first time in plasmas with neutral beam injection (NBI) heating alone at a low density of x l0re m 3 1t61, regardless the direction of beam (in co, counter and balanced injections). This is because the beam ion loss due to the 15 l0 'n a0,lri oh tmode I \ r.t \.+'\, \ r\tr r u +elcchon root o elestron root rrriqn 1961 l}.\ 10.,/+ H+node 3 l 0 tls {cur} s t.2 p v8 (c) Lrnode u't Er*0 B Hmode v+ v+ Fig. l Radial profilesof poloidal rotationvelocityatthetransitionof (a) LmodetoH_modeinJFT2Mtokamak[10] (b) and ion rootto electron root in LHD Heliotron plasmas t161. (c), (d) Flow patterns in tokamak H_mode plasmas and Helical electron root plasmas 37

3 IdaK. et al.. Structure of the Radial Electric Field and Toroidal/Poloidal Flow in High Temperature Toroidal Plasma drift orbit is small enough compared with the neoclassical non ambipolar loss. In previous experiments [1721], the transition from ion root to electron root was observed only in plasmas with ECH' therefore it has been also open to question as to whether the nonthermal electrons driven by ECH are required to achieve the transition. The transition of the radial electric field from ion root to electron root clearly demonstrates that nonthermal electrons are not necessary for the transition, because there are no nonthermal electrons in NBI heated plasma. The edge radial electric field sharply increases up to 15 kv/m in the electron root as the electron density is decreased while the absolute values increase gradually up to 5 kv/m in the ion root over a wide range of electron density of x 101e m3. The transition of poloidal flow in the electron diamagnetic direction (negative E.) to flow in the ion diamagnetic direction (positive E) is observed at p > 0.85 and there is no large poloidal flow observed in the plasma core. The absolute values of poloidal flow measured in the electron or ion root are the levels predicted by neoclassical theory [3]. 3. Spontaneous Toroidal Flow The toroidal flow has been considered to be determined by the radial transport of momentum driven by neutral beam injection (NBI) with anomalous shear viscosity. Although the E x B velocity shear due to the toroidal flow can be important in the plasma core, there have been few experiments that demonstrate a spontaneous toroidal flow not driven by NBI in tokamaks It is generally the case in tokamaks that the plasma rotates parallel (antiparallel) to the plasma current for the coinjected (counterinjected) NBI, which corresponds to a positive (negative) radial electric field (Er) in Lmode plasmas. However, when a negative Er is produced at the transport barrier, both localized toroidal flow in the counterdirection and localized poloidal flow in the electron diamagnetic direction are observed even for plasmas with coinjected NBI t26,271. These results show the need for detailed measurements of both toroidal and poloidal flow at the transport barrier, where the toroidal flow profile is not determined by the transport of momentum driven by NBI alone. 3.1 Spontaneous Toroidal Flow in Tokamaks A nondiffusive term in the toroidalmomentumtransport equation is evaluated by the analysis of the transport of toroidal rotation in the transient phase, where the direction of neutral beam injection is changed from parallel to the plasma current to antiparallel' Nondiffusive momentum transport is found to be in proportion to VTi. Figure 2 displays time evolution and radial profiles for discharges when the direction of the NBI is revers ed at t = 750 with a plasma current of 243 ka. The coinjection is activated from 550 to 750 and the counterinjection from 750 to 950 in Figs. 2(a) and 2(c) and the counternbl is activated from 600 to 750 and the conbi from 750 to 950 in Figs. 2(b), 2(d)' The toroidal rotation velocity changes its sign depending on the direction of the beam. The rapid changes in toroidal rotation velocity after t = 750 are due to the switching of beam direction from coinjection (driving positive toroidal rotation) to counterinjection (driving negative toroidal rotation) or from counterinjection to coinjection. Gradual changes in toroidal rotation velocity afterwards (800 ) are due to the improvement of momentum confinement associated with density peaking. Although the absorbed momenta of the beam are adjusted to be almost identical (injected power of ctrnbi is larger than that of conbi)' the toroidal rotation velocity near the plasma center (R = 1.35 m) in counterinjection is almost twice of that in coinjection. The gradient of toroidal rotation velocity estimated from the difference of toroidal rotation velocity between R = 1.4 m and R = 1.5 m (indicated with arrows in Figs. 2(a) and 2(b)) in counterinjection is 23 times larger than that in coinjection. Figure 2 (c)' (d) displays profiles of toroidal momentum (mlnivq) for discharges when the direction of the injected neutral beam changes from co to counter and from counter to co at the flat top of the plasma current (/ = 750 )' Here, mi is the ion mass and n; is the ion density of deutrons. As shown in Fig. 3(a), the differences of toroidal rotation velocity between coinjection and counterinjection becomes small, when the plasma current, /o, is increased (poloidal field is also increased). Figure 3(b) shows the offdiagonal coefficient given by the slope in Fig. 3(a) as a function of plasma current' The offdiagonal coefficients derived at p = 0.46 using the transport analysis are also plotted for comparison. This agreement suggests the validity of assumption of f(conbi) = f(ctrnbi) and that the differences in the magnitude and profile of momentum input between coinjection and counterinjection can be ignored. The offdiagonal coefficient decreases as the plasma current, 10, is increased. It is not clear whether the offdiagonal term will disappear or simply decrease as proportional to llle 38

4 IdaK. et al., Structure of the Radial Electric Field and Toroidal/Poloidal Flow in High Temperature Toroidal plasma o E u J=to 100 (*) ' i t.5o rn:243ka 4lxg =1ail (b) Til 100 5n +0 t scn > JU 100 p =243kA ';i.4 I f l{a LJV ? time () 80 co to ck 0 q e F go d pp.?.6 '? r o?90.d _51 +!' 150f.'..,, ? nme ctr to co 4'757 " J. o f 7' * m5 Fig.2(a),(b) Timeevolutionof toroidal rotationvelocityatr=1.!g, 1, 1.45,1.S0, 1.55, 1.60mand(c),(d) radial profiles of toroidal momentum during the transient phase for discharges when the direction of the NBI is reversed. (a), (c) The coinjection is activated from 550 to 750 and the counterinjection from 750 to g50 ' (b), (d) The counternbl is activated from 550 to 750 and the conbl from 750 to 950 [24]. when the plasma current is increased above 350 ka. The range of plasma current available in the JFT2M is not wide enough to conclude the Ip dependence of the offdiagonal coefficients. If this current dependence is due to the drift orbit physics, the offdiagonal term should disappear in the plasma with large minor radius and large plasma current, where the drift orbit loss is negligible. However, the offdiagonal term of toroidal momentum is observed in the large tokamak with a large plasma current [28]. Therefore the offdiagonal term is considered to be not due to the orbit physics and it is general characteristic in tokamaks regardless the size of plasma or plasma current. The plasma current dependence of the offdiagonal coefficient observed in JFT2M at least supports the hypothesis that the offdiagonal coefficient is proportional to lllo or llbo. The ratio of nondiffusive viscosity coefficient to diffusive viscosity coefficient is evaluated to be 0.1 to 0.3, which increases as the plasma current is decreased. 3.2 Spontaneous Toroidal Flow in Helical System A toroidal flow antiparallel to the <E. x Be > drift direction is observed in the hot electron mode plasmas when a large positive electric field and a sharp electron temperature gradient are sustained inside the internal transport barrier in the Compact Helical System (CHS) [29]. This toroidal flow reaches up to 5 x 104 m/s at the plasma center and it is large enough to reverse the toroidal flow driven by tangentially injected neutral beam. These observations clearly show that the plasma favors flow in the minimum VB direction at the transport barrier. The reversal of toroidal flow is observed when the 2 nd ECH pulse (r = 601, Pur, = 0.11 MW) is applied to the NBI plasma (t = l2o0 E167 = 36 kv 39

5 ldak. et al., Structure of the Radial Electric Field and Toroidal/Poloidal Flow in High Temperature Toroidal Plasma 50 t0 =l+jkfi r.ii]juf Kfl :242kA Eri:155 ka :243kA.d Ip:258k4 tr tt *t \E E a* {\ = e a (b) l0 _+ offdiagonal tr offdiagonal trans l dt,/dr (lrev/m) r rp (ka) 35u (c) Spantaneou$ flow. "2.t'" {d) large Ip p 0 Fig. 3 (a) The difference of gradient of toroidal rotation velocity between coinjection and counter injection as a function of the gradient of ion temperature at R = 1.45 m (p = 0.46) for discharges with the various plasma current. (b) Offdiagonal coefficient a function of plasma current with a simple formula and with a transport analysis [2a] (c), (d) relation of plasma flow respect to the direction of magnetic field for large and small plasma current (lo). PNil = O.7 MW) with low electron density below 0.7 x lgte.3. Hete p is the normalized averaged minor radius (p = rla).the electron temperature increases up to 2 kev (hot electron mode), while it is only 0.2 kev when there is no 2nd ECH pulse, which indicates a significant improvement in electron confinement during the 2nd ECH pulse, the electron collisionality is low enough to make the plasma to be in the electron root (positive electric field). The positive radial electric field is mainly contributed by the poloidal flow in the direction parallel to the <E, x Bo> drift. The Lorenz forces due to the toroidal flow and the force due to the ion pressure are negligible in the radial force balance [30]. The Lorenz force due to the poloidal flow is almost balanced with the force due to the radial electric field and therefor the magnitude of Er is roughly equal to vsb6 in CHS plasmas. The radial electric field derived from plasma flow with the radial force balance agrees well with that measured with HIBP [31]. The large electric field of 1020 kv/m and the large poloidal flow of 1020 km/s are produced near the plasma center (p = 0.3) [Fig. a(a)]. The neutral beam is injected to the plasma tangentially in the codirection. Here the "co" direction (positive flow velocity) is defined as parallel to the equivalent toroidal plasma current, which would produce the average transform actually produced by the external coil current. The "counter" direction (negative flow velocity) is defined as antiparallel to the equivalent toroidal plasma current. As seen in Fig. 4(b), the plasma rotates parallel to the NBI when there is no 2nd ECH. This is simply because the toroidal momentum from the NBI causes the plasma toroidal flow. However, when the 2nd ECH is turned on, the toroidal flow velocity decreases and finally the plasma rotates antiparallel to the NBI. These measurements clearly show the driven toroidal flow associated with a large poloidal flow (and large positive radial electric

6 IdaK. et al., Structure of the Radial Electric Field and Toroidal/Poloidal Flow in High Temperature Toroidal Plasma trn FJ 10 1{ rarith 2ndECH o no 2nd ECH 0.2 {B} ' 10 En & >alo = L mode x * o J r Y*r+ t el?ctron mode +rarith 2ndECH D CoNBI Fig. 4 Radial profiles of poloidal flow velocity at t = 110 and (b) toroidal flow velocity at t = 110 for the discharges with and without 2nd ECH pulse [29]. (c) ModB contour and flow pattern at p = 0.3 in CHS. The arrows stand for the flows in plasmas for NBI and NBI + ECH discharges. field) during the 2nd ECH pulse. The driven toroidal flow reaches 5 x 104 m/s at the plasma center and it is large enough to overcome the toroidal flow driven by tangentially injected neutral beam. It should be emphasized that the direction of the toroidal flow is antiparallel to the direction of <E. x Be> drift. This fact has not been predicted before, because a simple analogy from the experiments in tokamaks implies that the direction of the toroidal flow associated with a large radial electric field is parallel to the direction of <Er x Be > drift. This is because the toroidal viscosity is nearly zero due to the toroidal symmetry and the direction of the toroidal flow is simply determined by the direction of the <E. x 86 > drift in most discharges in tokamaks. 4, Discussion Although the transition of radial electric field and poloidal flow and spontaneous toroidal flow are observed both in tokamak and helical plasmas, there are differences in the direction of flows. The transition of poloidal flow observed in the Hmode in tokamaks is the jump of poloidal flow to the electron diamagnetic direction associated with the sudden increase of negative radial electric field shear. The turbulence levels in the plasma are also reduced as predicted by the anomalous transport models. On the other hand, the transition of poloidal flow observed in helical plasma is the change from electron diamagnetic direction to the ion diamagnetic direction, which is due to the reduction of ripple loss by large radial electric fields as predicted by the neoclassical theory. The spontaneous toroidal flows are observed in tokamak and helical plasmas. They become more significant at the transport barrier where the ion or electron pressure gradients become large. The spontaneous toroidal flow in tokamaks is parallel to the direction of <C, x Be> drift, while the spontaneous toroidal flow in helical plasmas is antiparallel to the direction of <E, x Be ) drift. This difference in the direction of spontaneous toroidal flow is due to the 4l

7 IdaK. et al., Structure of the Radial Electric Field and Toroidal/Poloidal Flow in High Temperature Toroidal Plasma difference of symmetry of magnetic field configuration. Since the plasma tends to flow along the minimum VB direction, where the parallel viscosity becomes minimum, the spontaneous toroidal flow in tokamak is always parallel to the <E. x Be> drift direction. In helical plasmas, the spontaneous flow has spiral structure due to the helical symmetry and the toroidal flow can be antiparallel to the <E,x Be > drift direction depending on the direction of pitch of spiral structure. In conclusion, the spontaneous poloidal and toroidal flow are observed in tokamak and helical plasmas associated with the large positive or negative radial electric field near the transport barrier. The understanding of the mechanism to drive the spontaneous poloidal and toroidal flow will be the key issue in the research of confinement improvement of high temperature toroidal plasmas. References tll K. Itoh and SI. Itoh, Plasma Phys. Control. Fusion 3E, (1996) 1. I2l t3l F.L. Hinton and D. Hazeltine, Rev. Mod. Phys. 4E, ( S.P. Hirshman and D.J. Sigmar, Nucl. Fusion 21, (l981) t4l H. Maassbeg et al.,plasma Phys. Control. Fusion 35, (1993) [5] F. Wagner et al., Phys. Rev. Lett. 49, (1982) 18. t6l s.i. Itoh and K. Itoh, Phys. Rev. Lett. 60, (1988) [7] K.C. Shaing and E.C. Crume Jr, Phys. Rev. Lett. 63, (1989) tsl R.J. Groebner, K.H. Burrell and R.P. Seraydarian, Phys. Rev. Lett. 64, (1990) t9l K. Ida, S. Hidekuma, Y. Miura et al., Phys. Rev. Lett.65, (1990) t10l K. Ida, S. Hidekuma, M. Kojima, Y. Mrura et al., Phys. Fluids. 94 (1992) [1] A.R. Field, G. Fussmann, J.V. Hofmann and the ASDEX team, Nucl. Fusion 43, (1992) ll9l. tl2l H. Biglari, P.H. Diamond and P.W. Terry, Phys. Fluids B 2. (1990) l. t13l K.C. Shaing, E.C. Crume Jr. and W.A. Houlberg, Phys. Fluids B 2, (1990) ll4l K.H. Burrell, Phys Plasmas 4, (1997) ll5le.j. Synakowski et al.,phy. Rev. Lett. 78, (1997) tl6l K. Ida, H. Funaba, S. Kado et al.,phys. Rev. Lett. 86, (200r) s297. [17] H. Idei, K. Ida, H. Sanuki et al.,phys. Rev. Lett. 7r, {1993) tl8l A. Fujisawa, H. Iguchi, T. Minami et al., Rev. Lett. 81, (1998) [19] J. Baldzuhm et al., Plasma Phys. Control., (1998) 967. Phys. Fusion t20l A. Fujisawa, H. Iguchi, T. Minami et al., Phys. Rev. Lett. 82, (1999) [21] H. Maassberg, C.D. Beidler, U. Gasparino et al., Phys. Plasmas 7, (2000) 295. t22lk. Nagashima, Y. Koida and H. Shirai, Nucl. Fusion 34, (1994) 449. t23lk.ida, Y. Miura et al., Phys. Rev. Lett. 74, (1995) t24lk. Ida, Y. Miura et a/., J. Phys. Soc. Jpn. 67, (1998) 89. I25l J.E. Rice e/ a/., Nucl. Fusion 38, (1998) 75 t26ly. Koide and JT60U Team, Phys. Plasmas 4, (1997) t27l R.E. Bell, F.M. Levinton et al.,phys. Rev. Lett. 81, (1998) l28l K. Nagashima, Nucl. Fusion 34, (1994) 449. l29lk. Ida, T. Minami et al.,to be published in Phys. Rev. Lett. 86, (2001) 30. t30l K. Ida, H. Yamada, H. Iguchi et al.,phys.7 Fluids B 3, (1991) 515. [31] K. Ida, A. Fujisawa, H. Iguchi et al.,phys. Plasma 8, (2001) r. A1